The Yorkshire giants tried to tempt Salzburg to sell Aaronson in the January transfer window, but the Austrian side were not willing to do business.
Leeds have been clear that they still want to sign the midfielder and have been waiting to secure their Premier League status in order to push a deal through.
Now they are finalising the capture of Aaronson, 21, and will look to quickly put the finishing touches to the deal.
The deal was agreed in principle on the condition that Leeds survive and will see the Whites pay Salzburg a fee of $30m to sign him.
Leeds have just survived in the Premier League and fans will be keen for the club to splash cash in the transfer market over the summer to avoid another season of struggle.
The club are tipped to lose star winger Raphinha, who is wanted by Barcelona.
Kalvin Phillips could also be on the move in the approaching summer transfer window, amid interest from several Premier League clubs.
